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Mohanty V, Louis AA. Robustness and stability of spin-glass ground states to perturbed interactions. Phys Rev E 2023; 107:014126. [PMID: 36797942 DOI: 10.1103/physreve.107.014126] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/10/2020] [Accepted: 12/16/2022] [Indexed: 06/18/2023]
Abstract
Across many problems in science and engineering, it is important to consider how much the output of a given system changes due to perturbations of the input. Here, we investigate the glassy phase of ±J spin glasses at zero temperature by calculating the robustness of the ground states to flips in the sign of single interactions. For random graphs and the Sherrington-Kirkpatrick model, we find relatively large sets of bond configurations that generate the same ground state. These sets can themselves be analyzed as subgraphs of the interaction domain, and we compute many of their topological properties. In particular, we find that the robustness, equivalent to the average degree, of these subgraphs is much higher than one would expect from a random model. Most notably, it scales in the same logarithmic way with the size of the subgraph as has been found in genotype-phenotype maps for RNA secondary structure folding, protein quaternary structure, gene regulatory networks, as well as for models for genetic programming. The similarity between these disparate systems suggests that this scaling may have a more universal origin.
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Affiliation(s)
- Vaibhav Mohanty
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford, OX1 3NP, United Kingdom
- MD-PhD Program and Program in Health Sciences and Technology, Harvard Medical School, Boston, Massachusetts 02125, USA and Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Ard A Louis
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford, OX1 3NP, United Kingdom
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Jiang K, Qiao J, Lan Y. Chaotic renormalization flow in the Potts model induced by long-range competition. Phys Rev E 2021; 103:062117. [PMID: 34271755 DOI: 10.1103/physreve.103.062117] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2021] [Accepted: 05/19/2021] [Indexed: 11/07/2022]
Abstract
A proper description of spin glass remains a hard subject in theoretical physics and is considered to be closely related to the emergence of chaos in the renormalization group (RG) flow. Previous efforts concentrate on models with either complicated or nonrealistic interactions in order to achieve this chaotic behavior. Here we find that the commonly used Potts model with long-range interaction could do the job nicely in a large parameter regime as long as the competition between the ferromagnetic and antiferromagnetic interaction is maintained. With this simplicity, the appearance of chaos is observed to sensitively depend on the detailed network structure: the parity of bond number in a branch of the basic RG substituting unit; chaos only emerges for even numbers of bonds. These surprising and universal findings may shed light on the study of spin glass.
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Affiliation(s)
- Kejin Jiang
- School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
| | - Jianyong Qiao
- School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
| | - Yueheng Lan
- School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China.,State Key Lab of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China
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Çağlar T, Berker AN. Phase transitions between different spin-glass phases and between different chaoses in quenched random chiral systems. Phys Rev E 2017; 96:032103. [PMID: 29346860 DOI: 10.1103/physreve.96.032103] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2017] [Indexed: 11/07/2022]
Abstract
The left-right chiral and ferromagnetic-antiferromagnetic double-spin-glass clock model, with the crucially even number of states q=4 and in three dimensions d=3, has been studied by renormalization-group theory. We find, for the first time to our knowledge, four spin-glass phases, including conventional, chiral, and quadrupolar spin-glass phases, and phase transitions between spin-glass phases. The chaoses, in the different spin-glass phases and in the phase transitions of the spin-glass phases with the other spin-glass phases, with the non-spin-glass ordered phases, and with the disordered phase, are determined and quantified by Lyapunov exponents. It is seen that the chiral spin-glass phase is the most chaotic spin-glass phase. The calculated phase diagram is also otherwise very rich, including regular and temperature-inverted devil's staircases and reentrances.
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Affiliation(s)
- Tolga Çağlar
- Faculty of Engineering and Natural Sciences, Sabancı University, Tuzla, Istanbul 34956, Turkey
| | - A Nihat Berker
- Faculty of Engineering and Natural Sciences, Kadir Has University, Cibali, Istanbul 34083, Turkey.,Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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Çağlar T, Berker AN. Devil's staircase continuum in the chiral clock spin glass with competing ferromagnetic-antiferromagnetic and left-right chiral interactions. Phys Rev E 2017; 95:042125. [PMID: 28505813 DOI: 10.1103/physreve.95.042125] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/10/2016] [Indexed: 11/07/2022]
Abstract
The chiral clock spin-glass model with q=5 states, with both competing ferromagnetic-antiferromagnetic and left-right chiral frustrations, is studied in d=3 spatial dimensions by renormalization-group theory. The global phase diagram is calculated in temperature, antiferromagnetic bond concentration p, random chirality strength, and right-chirality concentration c. The system has a ferromagnetic phase, a multitude of different chiral phases, a chiral spin-glass phase, and a critical (algebraically) ordered phase. The ferromagnetic and chiral phases accumulate at the disordered phase boundary and form a spectrum of devil's staircases, where different ordered phases characteristically intercede at all scales of phase-diagram space. Shallow and deep reentrances of the disordered phase, bordered by fragments of regular and temperature-inverted devil's staircases, are seen. The extremely rich phase diagrams are presented as continuously and qualitatively changing videos.
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Affiliation(s)
- Tolga Çağlar
- Faculty of Engineering and Natural Sciences, Sabancı University, Tuzla, Istanbul 34956, Turkey
| | - A Nihat Berker
- Faculty of Engineering and Natural Sciences, Sabancı University, Tuzla, Istanbul 34956, Turkey.,Faculty of Engineering and Natural Sciences, Kadir Has University, Cibali, Istanbul 34083, Turkey.,Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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Çağlar T, Berker AN. Chiral Potts spin glass in d=2 and 3 dimensions. Phys Rev E 2016; 94:032121. [PMID: 27739736 DOI: 10.1103/physreve.94.032121] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2016] [Indexed: 11/07/2022]
Abstract
The chiral spin-glass Potts system with q=3 states is studied in d=2 and 3 spatial dimensions by renormalization-group theory and the global phase diagrams are calculated in temperature, chirality concentration p, and chirality-breaking concentration c, with determination of phase chaos and phase-boundary chaos. In d=3, the system has ferromagnetic, left-chiral, right-chiral, chiral spin-glass, and disordered phases. The phase boundaries to the ferromagnetic, left- and right-chiral phases show, differently, an unusual, fibrous patchwork (microreentrances) of all four (ferromagnetic, left-chiral, right-chiral, chiral spin-glass) ordered phases, especially in the multicritical region. The chaotic behavior of the interactions, under scale change, are determined in the chiral spin-glass phase and on the boundary between the chiral spin-glass and disordered phases, showing Lyapunov exponents in magnitudes reversed from the usual ferromagnetic-antiferromagnetic spin-glass systems. At low temperatures, the boundaries of the left- and right-chiral phases become thresholded in p and c. In d=2, the chiral spin-glass Potts system does not have a spin-glass phase, consistently with the lower-critical dimension of ferromagnetic-antiferromagnetic spin glasses. The left- and right-chirally ordered phases show reentrance in chirality concentration p.
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Affiliation(s)
- Tolga Çağlar
- Faculty of Engineering and Natural Sciences, Sabancı University, Tuzla, Istanbul 34956, Turkey
| | - A Nihat Berker
- Faculty of Engineering and Natural Sciences, Sabancı University, Tuzla, Istanbul 34956, Turkey.,Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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Unraveling Quantum Annealers using Classical Hardness. Sci Rep 2015; 5:15324. [PMID: 26483257 PMCID: PMC4611884 DOI: 10.1038/srep15324] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2015] [Accepted: 09/22/2015] [Indexed: 11/08/2022] Open
Abstract
Recent advances in quantum technology have led to the development and manufacturing of experimental programmable quantum annealing optimizers that contain hundreds of quantum bits. These optimizers, commonly referred to as 'D-Wave' chips, promise to solve practical optimization problems potentially faster than conventional 'classical' computers. Attempts to quantify the quantum nature of these chips have been met with both excitement and skepticism but have also brought up numerous fundamental questions pertaining to the distinguishability of experimental quantum annealers from their classical thermal counterparts. Inspired by recent results in spin-glass theory that recognize 'temperature chaos' as the underlying mechanism responsible for the computational intractability of hard optimization problems, we devise a general method to quantify the performance of quantum annealers on optimization problems suffering from varying degrees of temperature chaos: A superior performance of quantum annealers over classical algorithms on these may allude to the role that quantum effects play in providing speedup. We utilize our method to experimentally study the D-Wave Two chip on different temperature-chaotic problems and find, surprisingly, that its performance scales unfavorably as compared to several analogous classical algorithms. We detect, quantify and discuss several purely classical effects that possibly mask the quantum behavior of the chip.
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Ilker E, Berker AN. Overfrustrated and underfrustrated spin glasses in d=3 and 2: evolution of phase diagrams and chaos including spin-glass order in d=2. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:042139. [PMID: 24827224 DOI: 10.1103/physreve.89.042139] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/27/2013] [Indexed: 06/03/2023]
Abstract
In spin-glass systems, frustration can be adjusted continuously and considerably, without changing the antiferromagnetic bond probability p, by using locally correlated quenched randomness, as we demonstrate here on hypercubic lattices and hierarchical lattices. Such overfrustrated and underfrustrated Ising systems on hierarchical lattices in d=3 and 2 are studied. With the removal of just 51% of frustration, a spin-glass phase occurs in d=2. With the addition of just 33% frustration, the spin-glass phase disappears in d=3. Sequences of 18 different phase diagrams for different levels of frustration are calculated in both dimensions. In general, frustration lowers the spin-glass ordering temperature. At low temperatures, increased frustration favors the spin-glass phase (before it disappears) over the ferromagnetic phase and symmetrically the antiferromagnetic phase. When any amount, including infinitesimal, frustration is introduced, the chaotic rescaling of local interactions occurs in the spin-glass phase. Chaos increases with increasing frustration, as can be seen from the increased positive value of the calculated Lyapunov exponent λ, starting from λ=0 when frustration is absent. The calculated runaway exponent yR of the renormalization-group flows decreases with increasing frustration to yR=0 when the spin-glass phase disappears. From our calculations of entropy and specific-heat curves in d=3, it is shown that frustration lowers in temperature the onset of both long- and short-range order in spin-glass phases, but is more effective on the former. From calculations of the entropy as a function of antiferromagnetic bond concentration p, it is shown that the ground-state and low-temperature entropy already mostly sets in within the ferromagnetic and antiferromagnetic phases, before the spin-glass phase is reached.
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Affiliation(s)
- Efe Ilker
- Faculty of Engineering and Natural Sciences, Sabancı University, Tuzla 34956, Istanbul, Turkey
| | - A Nihat Berker
- Faculty of Engineering and Natural Sciences, Sabancı University, Tuzla 34956, Istanbul, Turkey and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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Sasaki M, Hukushima K, Yoshino H, Takayama H. Scaling analysis of domain-wall free energy in the Edwards-Anderson Ising spin glass in a magnetic field. PHYSICAL REVIEW LETTERS 2007; 99:137202. [PMID: 17930628 DOI: 10.1103/physrevlett.99.137202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/13/2007] [Indexed: 05/25/2023]
Abstract
The stability of the spin-glass phase against a magnetic field is studied in the three- and four-dimensional Edwards-Anderson Ising spin glasses. Effective couplings J(eff) and effective fields H(eff) associated with length scale L are measured by a numerical domain-wall renormalization-group method. The results obtained by scaling analysis of the data strongly indicate the existence of a crossover length beyond which the spin-glass order is destroyed by field H. The crossover length well obeys a power law of H which diverges as H --> 0 but remains finite for any nonzero H, implying that the spin-glass phase is absent even in an infinitesimal field. These results are well consistent with the droplet theory for short-range spin glasses.
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Affiliation(s)
- M Sasaki
- Department of Applied Physics, Tohoku University, Sendai, 980-8579, Japan
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Katzgraber HG, Krzakała F. Temperature and disorder chaos in three-dimensional Ising spin glasses. PHYSICAL REVIEW LETTERS 2007; 98:017201. [PMID: 17358500 DOI: 10.1103/physrevlett.98.017201] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/07/2006] [Indexed: 05/14/2023]
Abstract
We study the effects of small temperature as well as disorder perturbations on the equilibrium state of three-dimensional Ising spin glasses via an alternate scaling ansatz. By using Monte Carlo simulations, we show that temperature and disorder perturbations yield chaotic changes in the equilibrium state and that temperature chaos is considerably harder to observe than disorder chaos.
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